1. Field of the Invention
The present invention relates to a strain wave gearing, and more particularly to an improvement of tooth profiles of a circular spline a flexspline used in the strain wave gearing.
2. Description of Prior Art
A strain wave gearing has been well known as seen from U.S. Pat. No. 2,906,143 granted to Musser. A typical strain wave gearing comprises a rigid circular spline, a flexspline having teeth which number more or less than that of the circular spline by 2n ("n" being a positive integer) and being disposed in the circular spline, and a wave generator disposed in the flexspline to deform the flexspline to, for example, an elliptic configuration so as to bring the flexspline into engagement with the circular spline at two points on the major axis of the ellipsoid. The wave generator includes an elliptic cam plate and a ball bearing fittingly mounted on the outer periphery of the cam plate. The outer wheel of the bearing is inserted into the flexspline to deform the flexspline to the elliptic shape. In the strain wave gearing as mentioned above, the input shaft fixed to the cam plate of the wave generator is rotated while the ellipsoid of the flexspline is rotated. Upon rotating the ellipsoid, one of the flexspline and the circular spline is rotated relative to the other by an amount that is in proportion to the difference in the number of the teeth between both splines. Where an output shaft is mounted on either the flexspline or the cicular spline, the output shaft is rotated very slowly in comparison with the input shaft. Thus, the strain wave gearing has frequently been applied to precision machinery because in the gearing, a high reduction ratio is obtained in spite of the low number of elements employed therefor.
Recent developments have been made with respect to teeth used in a strain wave gearing so as to improve engagement properties of the teeth to obtain a good performance and increase the load capacity. A basic gear tooth is disclosed in detail in U.S. Pat. No. 3,415,143 granted to Ishikawa, in detail. The tooth thereof is formed in a linear shape. Thus, the elliptic flexspline is engaged with the circular spline only at the points on the major axis of the ellipsoid, resulting in a lowering of the allowable transfer torque. The Ishikawa patent teaches that an involute tooth is applied to the gearing.
If the tooth of the Ishikawa patent is applied to the gearing, however, it is difficult to bring the flexspline into a continuous engagement with the circular spline until one of the splines is completely separated from the other. More specifically, in the case of a zero or negative deviation as shown in the curves a and c of FIG. 4 of the Ishikawa patent, the flexspline engaging with the rigid circular spline has a movement locus of the typical point of the tooth thereof (except a portion of the top of the curve c), the locus being concave with respect to the circular spline. In order to obtain the continuous contact between both splines, it is necessary that the profile of the tooth of the circular spline be formed convex in shape, unlike the linear tooth and the involute tooth. Where the movement locus of the typical point of the flexspline is convex (positive deviation) as shown in the curve b of FIG. 4 of the Ishikawa patent, deflection of the flexspline increases and then the bending stress increase. Thus, it is disadvantageous that the available range of the locus is small and that there are few teeth which are in mesh with each other. There is room for improving the strain wave gearings of the '143 patent with regard to allowable transfer torque.